Neural Unbalanced Optimal Transport via Cycle-Consistent Semi-Couplings

TL;DR

This paper introduces NubOT, a neural unbalanced optimal transport method using semi-couplings and cycle consistency to handle population changes, demonstrated on cancer cell response forecasting.

Contribution

The paper proposes NubOT, a novel neural unbalanced OT framework with a cycle-consistent training scheme for modeling population dynamics in unpaired data.

Findings

Improved accuracy in modeling cell proliferation and death.

Enhanced forecasting of cancer cell responses to drugs.

Outperforms previous neural OT methods.

Abstract

Comparing unpaired samples of a distribution or population taken at different points in time is a fundamental task in many application domains where measuring populations is destructive and cannot be done repeatedly on the same sample, such as in single-cell biology. Optimal transport (OT) can solve this challenge by learning an optimal coupling of samples across distributions from unpaired data. However, the usual formulation of OT assumes conservation of mass, which is violated in unbalanced scenarios in which the population size changes (e.g., cell proliferation or death) between measurements. In this work, we introduce NubOT, a neural unbalanced OT formulation that relies on the formalism of semi-couplings to account for creation and destruction of mass. To estimate such semi-couplings and generalize out-of-sample, we derive an efficient parameterization based on neural optimal transport maps and propose a novel algorithmic scheme through a cycle-consistent training procedure. We apply our method to the challenging task of forecasting heterogeneous responses of multiple cancer cell lines to various drugs, where we observe that by accurately modeling cell proliferation and death, our method yields notable improvements over previous neural optimal transport methods.